On basicity of the system of eigenfunctions of one discontinuous spectral problem for second order differential equation for grand-Lebesgue space


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Zeren Y. , Ismailov M., Sirin F.

TURKISH JOURNAL OF MATHEMATICS, vol.44, pp.1595-1611, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2003-20
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1595-1611
  • Keywords: Grand Lebesgue space, eigenfunctions, basicity, completeness, minimality, discontinuous spectral problem, PIECEWISE-LINEAR PHASE, MORREY, EXPONENTS

Abstract

Basicity of the system of eigenfunctions of some discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space L-p) (-1; 1) is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace G(p)) (-1;1) of L-p) (-1; 1) generated by shift operator is considered. Basicity of the system of eigenfunctions for the space G(p) )(-1;1)circle plus C, 1 < p < +infinity, is proved. It is shown that the system of eigenfunctions of considered problem forms a basis for G(p)()) (-1;1), 1 < p < +infinity, after removal of any of its even-numbered functions.